{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "GAN理论",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNBgjNDF0sWiOv/WE5WUQ8X",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/starhou/One-dimensional-GAN/blob/master/GAN%E7%90%86%E8%AE%BA.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mk-PC4elGD6I",
        "colab_type": "text"
      },
      "source": [
        "#对抗生成网络\n",
        "\n",
        " [ref.GAN](http://papers.nips.cc/paper/5423-generative-adversarial-nets.pdf)\n",
        " [ref.WGAN](https://arxiv.xilesou.top/pdf/1701.07875.pdf)\n",
        " [ref.郑华滨知乎博客](https://zhuanlan.zhihu.com/p/25071913)\n",
        " [ref.WGAN-GP](http://papers.nips.cc/paper/7159-improved-training-of-wasserstein-gans.pdf)\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eskuSQSFYP_h",
        "colab_type": "text"
      },
      "source": [
        "GAN的目标函数是\n",
        "\n",
        "$$\\min _{G} \\max _{D} V(D, G)=\\mathbb{E}_{\\boldsymbol{x} \\sim p_{\\text {data }}(\\boldsymbol{x})}[\\log D(\\boldsymbol{x})]+\\mathbb{E}_{\\boldsymbol{z} \\sim p_{\\boldsymbol{z}}(\\boldsymbol{z})}[\\log (1-D(G(\\boldsymbol{z})))].....(1)$$\n",
        "\n",
        "分析目标函数，其中对判别器$D$，其目标函数是：$E_{r}[logD(x)]+E_{g}[log(1-D(G(z))]$，对生成器G，其目标函数是：$E_{g}[log(1-D(G(z))]$。\n",
        "\n",
        "对判别器，一个样本的损失函数是\n",
        "$$\n",
        "-P_{r}(x) \\log D(x)-P_{g}(x) \\log [1-D(x)].....(2)\n",
        "$$\n",
        "\n",
        "首先最大化D(x)，对D(x)求导，得到$$D^{*}(x)=\\frac{P_{r}(x)}{P_{r}(x)+P_{g}(x)}.....(3)$$\n",
        "\n",
        "其含义是，最优判别器$D^{*}(x)$可以准确给出输入样本中真实样本所占的比例。把(3)带入判别器的损失函数(2)，得到\n",
        "\n",
        "$$\\mathbb{E}_{x \\sim P_{r}} \\log \\frac{P_{r}(x)}{\\frac{1}{2}\\left[P_{r}(x)+P_{g}(x)\\right]}+\\mathbb{E}_{x \\sim P_{g}} \\log \\frac{P_{g}(x)}{\\frac{1}{2}\\left[P_{r}(x)+P_{g}(x)\\right]}-2 \\log 2.....(4)(a)$$\n",
        "\n",
        "即为2倍JS散度，\n",
        "$$\n",
        "2 J S\\left(P_{r} \\| P_{g}\\right)-2 \\log 2.....(4)(b)\n",
        "$$\n",
        "\n",
        "原始GAN的损失函数是JS散度，对JS散度，当两个分布是不相交时，JS散度恒为为$log2$，如图1，对毫不重合的两个分布，JS散度为log2（[证明](https://blog.csdn.net/Invokar/article/details/88917214)）\n",
        "\n",
        "\n",
        "\n",
        "The Total Variation (TV) distance\n",
        "$$\\delta\\left(\\mathbb{P}_{r}, \\mathbb{P}_{g}\\right)=\\sup _{A \\in \\Sigma}\\left|\\mathbb{P}_{r}(A)-\\mathbb{P}_{g}(A)\\right|$$\n",
        "\n",
        "The Kullback-Leibler (KL) divergence\n",
        "$$K L\\left(\\mathbb{P}_{r} \\| \\mathbb{P}_{g}\\right)=\\int \\log \\left(\\frac{P_{r}(x)}{P_{g}(x)}\\right) P_{r}(x) d \\mu(x)$$\n",
        "\n",
        "The Jensen-Shannon (JS) divergence\n",
        "$$J S\\left(\\mathbb{P}_{r}, \\mathbb{P}_{g}\\right)=K L\\left(\\mathbb{P}_{r} \\| \\mathbb{P}_{m}\\right)+K L\\left(\\mathbb{P}_{g} \\| \\mathbb{P}_{m}\\right)$$\n",
        "\n",
        "其中$\\mathbb{P}_{m} = \\left(\\mathbb{P}_{r}+\\mathbb{P}_{g}\\right) / 2$\n",
        "\n",
        "The Earth-Mover (EM) distance or Wasserstein-1\n",
        "$$\n",
        "W\\left(\\mathbb{P}_{r}, \\mathbb{P}_{g}\\right)=\\inf _{\\gamma \\in \\Pi\\left(\\mathbb{P}_{r}, \\mathbb{P}_{g}\\right)} \\mathbb{E}_{(x, y) \\sim \\gamma}[\\|x-y\\|]\n",
        "$$\n",
        "\n",
        "对图1的分布，三种不同距离分别为，后两种距离不连续\n",
        "\n",
        "$\\cdot W\\left(\\mathbb{P}_{0}, \\mathbb{P}_{\\theta}\\right)=|\\theta|$\n",
        "\n",
        "$\\cdot J S\\left(\\mathbb{P}_{0}, \\mathbb{P}_{\\theta}\\right)=\\left\\{\\begin{array}{ll}\\log 2 & \\text { if } \\theta \\neq 0 \\\\ 0 & \\text { if } \\theta=0\\end{array}\\right.$\n",
        "\n",
        "$\\cdot K L\\left(\\mathbb{P}_{\\theta} \\| \\mathbb{P}_{0}\\right)=K L\\left(\\mathbb{P}_{0} \\| \\mathbb{P}_{\\theta}\\right)=\\left\\{\\begin{array}{ll}+\\infty & \\text { if } \\theta \\neq 0 \\\\ 0 & \\text { if } \\theta=0\\end{array}\\right.$\n",
        "\n",
        "由于推土机距离是计算下确界$inf$，很难计算，根据Kantorovich-Rubinstein duality(对偶)，具体计算，推土机距离满足下式\n",
        "$$\n",
        "W\\left(\\mathbb{P}_{r}, \\mathbb{P}_{\\theta}\\right)=\\sup _{\\|f\\|_{L} \\leq 1} \\mathbb{E}_{x \\sim \\mathbb{P}_{r}}[f(x)]-\\mathbb{E}_{x \\sim \\mathbb{P}_{\\theta}}[f(x)]\n",
        "$$\n",
        "距离计算变为求两个分布的期望差的上确界$\\sup$。个人理解，相较与下确界$\\inf$，$sup$的好处是，我们可以通过最小化两个分布的采样样本期望差来进行优化。这是因为目标是最小化其上确界，一般情况下的期望差必然更小\n",
        "\n",
        "WGAN算法：\n",
        "\n",
        "![](https://cdn.mathpix.com/snip/images/rMY6eF1AncGDOtt-U7X71q1H4yhqApnGsgQPk1OWS5M.original.fullsize.png)\n",
        "\n",
        "WGAN算法有一个混合真实样本和生成样本的步骤，判别器损失和原始GAN相同，生成器损失变为推土机距离。\n",
        "\n",
        "对WGAN-GP, WGAN对权值裁剪，WGAN-GP对梯度进行裁剪。原文中提到了一些梯度裁剪的好处如下\n",
        "\n",
        "```\n",
        "Gradient norms of deep WGAN critics during training on \n",
        "toy datasets either explode or vanish when using weight \n",
        "clipping, but not when using a gradient penalty. (right) \n",
        "Weight clipping (top) pushes weights towards two values \n",
        "(the extremes of the clipping range), unlike gradient \n",
        "penalty (bottom).\n",
        "```\n",
        "WGAN-GP的算法如下：\n",
        "![](https://cdn.mathpix.com/snip/images/R1aey4DNXGztq4x9Fv-yGEuprtZ6ZCcNgR48660NR9s.original.fullsize.png)\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WIKiFTmNWZGl",
        "colab_type": "code",
        "outputId": "677d8a32-f677-424b-e379-8dd80290804c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 563
        }
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy import stats\n",
        "mu = 0\n",
        "sd = 0.3\n",
        "t1 = np.linspace(-1,1,1000)\n",
        "t2 = np.linspace(2,4,1000)\n",
        "y1 = stats.norm(mu, sd).pdf(t1)\n",
        "y2 = stats.norm(mu, sd).pdf(t1)\n",
        "\n",
        "plt.figure(1)\n",
        "plt.plot(t1,y1)\n",
        "plt.plot(t2,y2)\n",
        "plt.title(\"Figure 1\")\n",
        "\n",
        "plt.figure(2)\n",
        "plt.plot(t1,y1)\n",
        "plt.plot(t1,y1+0.5)\n",
        "plt.title(\"Figure 2\")"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Figure 2')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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A26zP24PPXUJEHhCRAyJywOfz2fDS8aWl15rPrvLac1PoxdQUZtGkUy4qGnqbrMXKSO5w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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wkQXPQfvLrYthbJRdUMybC5I5v2UMF7aOtbVtf9SpcS0u6dSASUt2cTS7wN7G\nu98AbS+GeX+Hw5vsbVudlib6QJd3DL642dqLH/m6rYdsACb/tJv0nEL+OrytliH2kAeGtiG/uJS3\nFybb27AIjHwDqtWEL2+xhptUXkETfSAzxrr69UQqXDnZqmNio4ycQiYu3sWwDvXoZtfl+wGgVd0o\nrklszKcr9rE/I9fexqPqwuX/hiObtculF9FEH8hWfQibv4HBT0KTHrY3//bCZHILi3loaFvb2/Z3\n9wxujQj8a94O+xtvPQQufAjWfAJrPrW/ffU7mugDVepqmPkItBwIF9xrf/PH8vh4+V6u7N6Y1vVq\n2N6+v2tQK4IbLmjOV2tS2HYoy/4ABv7NurL6+wf1eL0X0EQfiLLT4LPrrRo2V74PQfZ/DP41dzsI\n3KeDilSZ2/u3IioshFfm2FjG+KSgYOuzVa0mTPuzNTqZcowm+kBTUgxf3GQNCTf6Y4iMsT2EHYez\n+HJ1Cn/u3YxGtSNsbz9QREeGcVv/lszdfJhVezPtD6BGPbhqMmTs0v71DtNEH2jmPQV7lsDIf1lD\nwznglTnbqB4Wwh0D4x1pP5Dc1McqY/zSLBvLGLtr3teqgLr1O1j0gv3tK0ATfWBZ8yksfwt63Apd\n/+hMCPsymb3pMGP7taROZJgjMQSSyPAQ7nGVMf5xu41ljN31vgO6XQeLJ2g9HIdoog8UuxbBt/dA\nywHWFYwOOFmGOCYyjJv72lcwLdCN6dGUJnUimDBrm71ljE8SsYaibHq+VWYjdZX9MQS4yo4ZO1xE\ntolIsog8Wsb810Rkreu2XUSOuc0rcZs3w5PBq0o6shU++zPEtIZrPrJqkzhgyY6jrNiVwd2D4okM\nr9QolsoDwkKCePCitmw+eILvNxx0JoiQcBj9CUTGwZQ/QuZeZ+IIUBUmehEJBt4GRgDtgWtFpL37\nMsaY+40xXY0xXYE3ga/cZuednGeMucyDsavKyDoMn14NodXgT9OgWi1HwigtNUyYvZXG0RFc26up\nIzEEssu6NCShfg3+OWcbRSUOnRSNjLU+g8V58MkVkHPUmTgCUGX26HsCycaYXcaYQmAqMOo0y18L\nTPFEcOoc5WXCJ1dC7lG4dirUdi7Bfr/hIBtTT/DARW0ID9FBRewWFCQ8PKwte9JzmZa037lA4trB\nH6fB8RRrB6Qg27lYAkhlEn0jwP2TkeKa9jsi0gxoASxwm1xNRJJEZIWIXF5eIyIy1rVcUlqaQyeN\n/ElBtvWPdHSb9ZO5UXfHQikqKeWfc7bRtl4NRnW1tzKm+p9BCXEkNovm9Xk7yCu0cXCSUzXtDVd/\nCAfXwbTrobjQuVgChKdPxoiUtJcAAB8wSURBVI4BvjDGuH+KmhljEoE/Av8SkVZlrWiMmWiMSTTG\nJNatW9fDYQWYonyYeq119etVkyF+sKPhTEvaz570XB4e1pZgLUPsGBHhkREJHMkq4MNle5wNpu0I\nq4jezgXw+Y2a7KtYZRJ9KtDE7Xlj17SyjOGUwzbGmFTX/S5gEeBM5+1AUZRvXYm4ezFc/i60G+lo\nOHmFJbw+bweJzaIZ3C7O0VgU9Gheh0EJcby7KJnjuTYOTlKW7tfDiJdh2/ea7KtYZRL9SqC1iLQQ\nkTCsZP673jMikgBEA8vdpkWLSLjrcSzQB9jsicBVGQpzYMoY2DEbLn0NuthbW74sHyzbzZGsAv46\nPEHLEHuJh4e1JaugmH8v3ul0KNBrrCZ7G1SY6I0xxcBdwGxgCzDNGLNJRJ4REfdeNGOAqea3l9+1\nA5JEZB2wEHjRGKOJvirkn7BOvO7+0dqTT/yL0xFxLLeQdxftZHBCHD1b1HE6HOXSrkFNRnVpyAdL\nd3P4RL7T4fw22X/2Jyi0ubRyABBHLouuQGJioklKSnI6DN+Rc9Q68XpovTV2Z8crnI4IgOd/2MJ/\nluxi5r0XklC/ptPhKDf70nMZ9M9FjO7RhH/8oZPT4ViSJsN3D0DjRKtnTnXdOTgTIrLKdT70d/TK\nWF93dAdMGmwN9DD6E69J8qnH8vhw2R6u6NZYk7wXahpTnWt7NmXqyv3sPprjdDiWxL/ANf+1euNM\nHm51wVQeoYnel+35CSYNsbpS3vCd1ZPBS/xr7nbAGtZOeae7B8UTFhzEq673yiu0HwXXfw1ZB63P\ntpZL8AhN9L5q9cfw0eVWTflb5zsyQlR5tmsZYp8QV7Maf+nbnG/XHWBj6nGnw/mf5n3hL7MgKBQm\nj4C1ev3ludJE72uK8mD6nTDjLmjeB26eA9HNnY7qNybM2kZkWAh3ahlirze2XytqRYTy8mwHBic5\nnXodYOwiaNITvhkHsx6zxlJQZ0UTvS9J3wmTLrLG4uz3MFz3FUR416DaK/dkMG/LYcYNaEW0liH2\nerUiQrljQCt+3J7Gil3pTofzW5Ex1mGcnrfBinfggxGQucfpqHySJnpfYAys/gje6w/H98MfP4dB\nT1jDtXkRYwwvztxKXI1wburT3OlwVCXdcEFz6tUMZ4JTg5OcTnAoXDzBGpYwbSv8+0LY8IXTUfkc\nTfTeLusQ/N9omHE3NOwK45ZAm6FOR1WmeVuOsGpvJvcOaU31MC1D7CuqhQZz35A2rN53jHlbjjgd\nTtk6XQXjfoK6CfDlzfDlLVr98gxoovdWpaXWXvw7va2LoIa/BH+e4WgFytMpLillwqyttIyN5JrE\nJhWvoLzK1ec1pmVsJC/P3kqJE4OTVEZ0M7hpJgx4DDZ9A2/1sE7UetuvEC+kid4bHVgL719k7cXX\nTbD2ZHqPgyDvfbs+S9rPjiPZPDysLaHB3hunKltIcBAPDG3D9sPZfLOmvFJWXiA4BAY8av2yjYm3\nTtR+fDkc1gvuT0f/I73J8RSYfhdMHADH9sEf3rP2YGJbOx3ZaWXlF/HqnO30bF6H4R3rOx2OOksX\nd2xAx0Y1eXXudgqKHSxjXBlx7eAvs+HiV+DAGvh3H/j2Xsj20kNPDtNE7w1yjsKsv8Eb3WH9Z9Zg\nyncnQZcx1nibXu6dRTtJzynkiUvbaeEyHxYUJDwyPMG6qnnpHqfDqVhQEPS8Fe5Za/XMWfMJvNEN\n5j8LOV7Wg8hhmuidlLkHfvgr/KsT/PwudLoa7l4Fw593bMi/M7U/I5f3f9rNFd0a0blxbafDUefo\nwtZ1GZQQx5sLkknLKnA6nMqpXgdGvAh3/gLxQ2DJP63/qTlPWkNpKk30tjMG9q2wSrK+0c0q5NT+\ncrhjBVz+tteebC3PhNnbCBJ4aFhbp0NRHvL4Je3ILyrh1bledhFVRWJaWbVy7lgBCRfD8rfgtQ5W\nD519Pwf0SVvtA2eX7DRYNwXWfAxHt0N4Tbjgbug1Dmo2dDq6s7JqbybfrjvAPYPiaailDvxGq7pR\n/Pn85nywbDfX9W5Gh4a+8evyV3EJcOUkq3fOL/+BtZ/Chs+hfmfodr1V+C8y1ukobaVliqtSzlHY\n+h1snm6N+FRaDI17WiPrdPgDhNdwOsKzZozhineXkZKZx6KHBhAZrvsM/uR4bhH9X1lIQv0aTLm1\nt2+feynIts59JU2GwxtBgqHVIOtQaZuhXnd1+dk6XZli/e/0pNJSOLQOdi2C5PmwdymYUohuAeff\nBV2utfY2/MB36w+yZt8xJlzZWZO8H6pVPZQHLmrD+OmbmLP5MMM6+HBvqvAo6HGzdTu8CdZPs66u\n/XqslfSbng9thlm32DY+0QHiTOke/bkoLoRDGyA1CfYth10/Ql6GNS+uPSRcYpVdrdfRrz48uYXF\nDP7nj0RXD+Pbu/vqgN9+qriklBGvL6GwpJQ59/cjPMS7Sm6ck9JSqwTy9pmwbRYc2WRNj4yDZhdA\nsz7WfVw7rys1Uh7do/eEvEw4stWqt3FkCxxYbQ2QUOIa47JGA2uPoOVAaNkfavjwHlAF3l6YzMHj\n+bx5bTdN8n4sJDiIJy9tz58n/8KHS/dwW/9WTofkOUFBVmnvJj1g8HjrupWdC2DvMtizFDZ/Yy0X\nEgH1O0GDLtatXgfrQq1qvjWYTqX26EVkOPA6EAxMMsa8eMr8G4GXgZOX1L1ljJnkmncD8IRr+nPG\nmP9W1J4je/QlxZB1AI7ttwqHHdsPx/Zat7RtkO3WTSs00nrTG58HjRKtoc9qNvKrvfby7D6aw7DX\nFnNp5wa8Orqr0+EoG/zlw5X8sjuDBQ/2J65mNafDqXrGWIl/33JrZ+7gOji4Hgqz/rdMVD2IaW31\n9IlpZf3/12xkdayo0QBC7K/cero9+goTvYgEA9uBi4AUYCVwrfsg365En2iMueuUdesASUAiYIBV\nwHnGmMzTtXnWid4YKMqFgqzf3wqzrfu8TMhJc92O/u9xboYrRDeRcVZ3x7ptXbd21jH2mo29uhxB\nVTHGcNOHK0nak8mCh/oTVyMA/unVr1/uF3eqz7/GdHM6HGeUlkLmbmvIzvRkOJps3afvgNxTL84S\na0CgqHpWH//qMRDhuq8eY00Lr2mdOwiLct3XgLBICI046x3Gcz100xNINsbscr3YVGAUUJniEsOA\nucaYDNe6c4HhQNUMGfOPBlCcV/Fy1Wpb3asi61rlBZpdANVjoVYjqNUEajezHodql0F387YcYdG2\nNJ64pJ0m+QDSIjaScf1b8saCZK7p0YQLWgVW10TA2rE7ufd+qvwTcOIAnEhx3R+wyplkH7HO2R3b\nZ+1I5h+ruJ3IOHh4h8fDr0yibwTsd3ueAvQqY7krRaQf1t7//caY/eWs26isRkRkLDAWoGnTs7xo\nqN+D1vBj4TX+940ZXsPtVtO6OfCzytflF5XwzHebaB0XxQ0XNHc6HGWzOwbG8/XaVJ78ZiMz7+1H\nWEjg/aItV7Wa1q2iHnUlxVayz00/5UhDtnVfmG31AqoCnjoZ+y0wxRhTICK3Af8FBp3JCxhjJgIT\nwTp0c1ZR9Hv4rFZTFXvvx13sz8jj/27tpdUpA1C10GCeuawjN324kvd/2s3tA/zoxKxdgkNcRxLs\n/0VUmf/YVMC9wHhj/nfSFQBjTLox5mRhjEnAeZVdV3m/XWnZvL0omUs7NwjMn+0KgIEJcQxtX483\n5u8gJTPX6XDUGahMol8JtBaRFiISBowBZrgvICIN3J5eBmxxPZ4NDBWRaBGJBoa6pikfYYzhb19v\nIDwkiPGXtnc6HOWw8SOtz8Az32r9d19SYaI3xhQDd2El6C3ANGPMJhF5RkQucy12j4hsEpF1wD3A\nja51M4Bnsb4sVgLPnDwxq3zD50kprNiVwd8ubhcYXevUaTWOrs49g1szZ/Nh5m7WypC+Qq+MVeVK\nyypgyKs/0rZeDaaO7U2QXhylgMLiUi576ycycwuZc39/akWEOh2S4vTdK/WsmirXM99tJq+whOev\n6KRJXv0qLCSIl67sTFpWAS/8sKXiFZTjNNGrMi3ceoRv1x3gzoHxxMdFOR2O8jJdmtTm1gtbMnXl\nfpYmH3U6HFUBTfTqd07kF/H41xuIj4ti3ICWToejvNT9F7WhRWwkj361ntzCYqfDUaehiV79zrPf\nbubQiXxeubqLf1UsVB5VLTSYF6/oxP6MPF6e7WOjUQUYTfTqN+ZtPsznq1K4Y0A8XZvoGLDq9Hq1\njOH63s34cNkeVu7RDnXeShO9+lVGTiGPfrWBhPo1uGdwa6fDUT7ikREJNI6O4IFpa8nKL3I6HFUG\nTfTqV09O38jxvEJeG91Va5moSosKD+G1a7qSmpnH3/VCKq+k/80KgOlrU/l+/UHuG9KGdg18a1AF\n5bzE5nW4c2A8X6xKYeaGg06Ho06hiV6xNz2Hx7/eyHnNormtn/ayUWfnnsGt6dy4Fo99vYHDJ/Kd\nDke50UQf4AqLS7lnyhqCBF4f05UQrUypzlJocBCvje5KflEJD32+jtJS77vqPlDpf3WAe2XONtal\nHGfCVZ1pHF3d6XCUj2tVN4rxl3ZgyY6jvL0w2elwlIsm+gC2aNsRJi7exXW9mzK8Y4OKV1CqEq7t\n2YRRXRvy2rztLNOrZr2CJvoAlZKZy/2fraVtvRo8cYmWH1aeIyI8/4dOtKwbxT1T1+jxei+giT4A\n5ReVMO6TVRSXGN69rjvVQvXqV+VZkeEhvPun7uQUlHD3lDUUl5Q6HVJA00QfYIwxPP71RjamnuDV\n0V1pWVcLlqmq0bpeDZ6/oiO/7M7gpVlbnQ4noHlqzFjlIz5ZsZcvV6dwz+DWXNS+ntPhKD/3h26N\nWbPvGP9Zsps29WpwdWKTildSHqd79AFk2c6j/P3bzQxKiOM+LXGgbPLkpe3pEx/D419vJEnr4ThC\nE32ASD6SxW0fr6JFbCSvje6qA4ko24QGB/H2H7vTsHY1xn2ySgcWd0ClEr2IDBeRbSKSLCKPljH/\nARHZLCLrRWS+iDRzm1ciImtdtxmnrquqXlpWATd+sJLwkGAm39hDh35TtqtdPYxJN/SgoLiUW/6b\nxAktfmarChO9iAQDbwMjgPbAtSJyan+8NUCiMaYz8AUwwW1enjGmq+t2GcpWeYUl3PJREkezC3j/\nhkSa1NGLopQz4uOiePdP57EzLZuxHyWRX1TidEgBozJ79D2BZGPMLmNMITAVGOW+gDFmoTHm5O+x\nFUBjz4apzkZRSSl3/d9q1qcc440x3eii9eWVw/q2juWVq7uwYlcG93+2lhItk2CLyiT6RsB+t+cp\nrmnluRmY6fa8mogkicgKEbm8vJVEZKxruaS0tLRKhKVOp6TU8MC0dczfeoRnR3VkaIf6ToekFACj\nujZi/KXtmbnxEOOnb8QYTfZVzaPdK0XkOiAR6O82uZkxJlVEWgILRGSDMWbnqesaYyYCEwESExP1\nnT8HVl/5DXy77gCPjUjgut7NKl5JKRv9pW8L0rILeHfRTqLCQ3h0RAIi2kGgqlQm0acC7p1fG7um\n/YaIDAEeB/obYwpOTjfGpLrud4nIIqAb8LtErzzDGMMz321m6sr93D0ontv6t3I6JKXK9Ndhbckp\nKOa9xbsANNlXocok+pVAaxFpgZXgxwB/dF9ARLoB7wHDjTFH3KZHA7nGmAIRiQX68NsTtcqDSksN\n42ds5JMV+/hLnxY8cFEbp0NSqlwiwt8v64AxaLKvYhUmemNMsYjcBcwGgoHJxphNIvIMkGSMmQG8\nDEQBn7vepH2uHjbtgPdEpBTrfMCLxhgda6wKFJeU8tcv1/PV6lTG9W/FI8Pb6j+M8noiwjOjOmAw\nvLd4F0UlhicuaafXeXhYpY7RG2N+AH44Zdp4t8dDyllvGdDpXAJUFSssLuX+z9by/YaDPHhRG+4a\nFK9JXvkMEeHZUR0JCQpi8tLdZOQUMOGqLjpusQdprRsfdyy3kNs+XsXPuzN44pJ23HKhDgWofI+I\n8NTI9tStEc7Ls7eRnlPIv687j8hwTVGeoF+ZPmxveg5XvLuMNfuO8fqYrprklU8TEe4cGM9LV3Zi\nafJRxkxcwaHjWsveEzTR+6iVezL4wzvLyMgp5NNbezGq6+kubVDKd4zu0ZSJ1yeyKy2bkW/9xKq9\nWgjtXGmi9zHGGCYt2cWYiSuoFRHK13f0oUfzOk6HpZRHDWlfj6/v7EP1sGDGTFzB1F/2OR2ST9NE\n70NO5Bdx+yeree77LQxpF8f0u/rQIjbS6bCUqhJt6tVg+p196N0yhke/2sBDn68ju6DY6bB8kiZ6\nH5G0J4ORb/7E3C2Hefzidvz7uvOoWU2rUCr/Vrt6GB/c2IO7B8Xz1eoULn1jCev2H3M6LJ+jid7L\n5ReV8MLMLVz93nJKSg1Tx/bm1n4ttfukChghwUE8OLQtU27tTUFxKVe+u4y3FuygSMehrTRN9F5s\n1d4MRr21lPd+3MWYHk2ZdV8/PR6vAlavljHMurcfwzrW55U52xn55k+s1b37ShFvrByXmJhokpKS\nnA7DMUezC3hx5la+WJVCg1rVeP6KTgxsG+d0WEp5jTmbDjF++iYOZ+Vzw/nNuX9IG2pVD+xDmSKy\nyhiTWNY8vRrBi+QXlfDJir28Pn8H+UUl3D6gFXcNjNeLRpQ6xdAO9Tm/VQwTZm3jv8v38M3aVO4d\n3JrrejcjNFgPVJxK9+i9QHFJKV+uTuH1eTs4cDyfC1vH8tTIDsTHRTkdmlJeb9OB4zz/wxaWJqfT\nIjaS+4a05tLODQkOsHo5p9uj10TvoPyiEr5cncKkJbvZfTSHLk1q88iwtlwQH+t0aEr5FGMMi7al\n8eLMrWw7nEXL2EjuGBjPqK4NA2YPXxO9lzmaXcCnK/bx0fI9pOcU0rlxLe4cGM/Q9vW0N41S56C0\n1DBn8yHemJ/M5oMnaFCrGtf1bsboHk2IjQp3OrwqpYneC5SUGhbvSGPayv3M3XyY4lLD4IQ4bu3X\nkl4t6miCV8qDjDEs3HaED5buYcmOo4QFB3Fxp/pc06MJvVvE+GUZZD0Z65DSUsOa/Zn8sOEQP2w4\nyMHj+dSJDOOmPs0Z3aOpHoNXqoqICIMS6jEooR7JR7L5ZMVevlyVwjdrD1C/ZjUu69qQy7o0pEPD\nmgGxk6V79B6WXVDMz7vS+XF7GrM3HeLwiQLCgoPo1yaWK7s3ZnC7elpnWykH5BWWMG/LYaavTWXR\ntjSKSw2NakcwKCGOQe3iOL9lDNVCg50O86zpoZsqlF1QzPr9x1i5J5OfktNYs+8YxaWGaqFBDGgT\nx4hO9RmUEEcNLVeglNfIyClk7uZDzN9yhCU7jpJXVEJ4SBDdm0bTq2UderaoQ/em0T6V+DXRe8ix\n3EJ2HMlm26Es1qccY+3+Y+w4ko0xIAKdGtWib3wsfeNj6d7Mtz4kSgWq/KISVuxKZ/H2o/y8O53N\nB09gDIQGC23r16Bjw1p0aFSLjg1rklC/JhFh3vl/fc6JXkSGA69jjRk7yRjz4inzw4GPgPOAdGC0\nMWaPa95jwM1ACXCPMWZ2Re05leiNMRzLLSIlM4/UY7mkZOaxPyOX5LRsth/OJi2r4Ndla1cPpWuT\n2r/eujWJDvgr85TyB8fzili1N4Nfdmey6cBxNqYeJzO36Nf5DWtVo0XdSFrGRtEiNpIWsZE0qF2N\nBjUjqBkR4tgx/3M6GSsiwcDbwEVACrBSRGacMsj3zUCmMSZeRMYALwGjRaQ9MAboADQE5olIG2NM\nybn9SRUzxlBQXEpWfjHZBcVku+6P5xVyNLuQ9OxC0nMKSM8u5Gh2Aek5hRw4lkdu4W9DiwoPoVVc\nFP3b1KV1XBRt6tUgPi6KxtERAXESR6lAUysi9NcTuWDlkgPH89mYepzth7LYfTSHnUdz+GZtKln5\nvy2bHBEaTINa1WhQuxpxNapRu3oo0dXDiI4MI7p6KHWqh1G7ehg1qoUQFR5CZHiILefsKtPrpieQ\nbIzZBSAiU4FRgHuiHwU87Xr8BfCWWFlwFDDVGFMA7BaRZNfrLfdM+L916ZtLyMwpshJ7QTElpaf/\ntVIrIpSYqDBiI8OJrxvFha1jaRxdnUa1I2gcbd1qRYRqQlcqgIkIjWpH0Kh2BMM61P91ujGG9JxC\n9qbncuh4PgeP57nu8zlwPI+kvRkcyykiq4Ia+mHBQUSGBxMZHkLDWhFMG3e+x/+GyiT6RsB+t+cp\nQK/yljHGFIvIcSDGNX3FKeuWOeadiIwFxgI0bdq0MrH/TnzdKILqCTXCQ4iqZn1bnnwcFR5KVHgI\nNSNCqBsVTnRkWMBcMaeU8jwRITYqvMILsQqLSzmWW0hmbhEZOYVk5hb+eoQhp6CY7MJicgtKyCko\nrrK9e6/pR2+MmQhMBOsY/dm8xr/GdPNoTEopda7CQoKIq1mNuJrVHIuhMl8fqUATt+eNXdPKXEZE\nQoBaWCdlK7OuUkqpKlSZRL8SaC0iLUQkDOvk6oxTlpkB3OB6fBWwwFjdeWYAY0QkXERaAK2BXzwT\nulJKqcqo8NCN65j7XcBsrO6Vk40xm0TkGSDJGDMDeB/42HWyNQPrywDXctOwTtwWA3fa0eNGKaXU\n/+gFU0op5QdO149eu50opZSf00SvlFJ+ThO9Ukr5OU30Sinl57zyZKyIpAF7z3L1WOCoB8PxFI3r\nzGhcZ0bjOjP+GFczY0zdsmZ4ZaI/FyKSVN6ZZydpXGdG4zozGteZCbS49NCNUkr5OU30Sinl5/wx\n0U90OoByaFxnRuM6MxrXmQmouPzuGL1SSqnf8sc9eqWUUm400SullJ/zyUQvIleLyCYRKRWRcrsi\nichwEdkmIski8qjb9BYi8rNr+meu8sueiKuOiMwVkR2u++gylhkoImvdbvkicrlr3ocistttXle7\n4nItV+LW9gy36U5ur64istz1fq8XkdFu8zy6vcr7vLjND3f9/cmu7dHcbd5jrunbRGTYucRxFnE9\nICKbXdtnvog0c5tX5ntqU1w3ikiaW/u3uM27wfW+7xCRG05dt4rjes0tpu0icsxtXpVsLxGZLCJH\nRGRjOfNFRN5wxbxeRLq7zTv3bWWM8bkb0A5oCywCEstZJhjYCbQEwoB1QHvXvGnAGNfjfwO3eyiu\nCcCjrsePAi9VsHwdrLLO1V3PPwSuqoLtVam4gOxypju2vYA2QGvX44bAQaC2p7fX6T4vbsvcAfzb\n9XgM8JnrcXvX8uFAC9frBNsY10C3z9DtJ+M63XtqU1w3Am+VsW4dYJfrPtr1ONquuE5Z/m6s0utV\nvb36Ad2BjeXMvxiYCQjQG/jZk9vKJ/fojTFbjDHbKljs10HNjTGFwFRglIgIMAhrEHOA/wKXeyi0\nUa7Xq+zrXgXMNMbkeqj98pxpXL9yensZY7YbY3a4Hh8AjgBlXv13jsr8vJwm3i+Awa7tMwqYaowp\nMMbsBpJdr2dLXMaYhW6foRVYI7lVtcpsr/IMA+YaYzKMMZnAXGC4Q3FdC0zxUNvlMsYsxtqpK88o\n4CNjWQHUFpEGeGhb+WSir6SyBjVvhDVo+TFjTPEp0z2hnjHmoOvxIaBeBcuP4fcfsn+4frq9JiKn\nH3XY83FVE5EkEVlx8nASXrS9RKQn1l7aTrfJntpe5X1eylzGtT2OY22fyqxblXG5uxlrz/Ckst5T\nO+O60vX+fCEiJ4cV9Yrt5TrE1QJY4Da5qrZXRcqL2yPbymsGBz+ViMwD6pcx63FjzHS74znpdHG5\nPzHGGBEpt++q69u6E9bIXSc9hpXwwrD60z4CPGNjXM2MMaki0hJYICIbsJLZWfPw9voYuMEYU+qa\nfNbbyx+JyHVAItDfbfLv3lNjzM6yX8HjvgWmGGMKROQ2rF9Dg2xquzLGAF+Y34565+T2qjJem+iN\nMUPO8SXKG5g8HetnUYhrr+yMBiw/XVwiclhEGhhjDroS05HTvNQ1wNfGmCK31z65d1sgIh8AD9kZ\nlzEm1XW/S0QWAd2AL3F4e4lITeB7rC/5FW6vfdbbqwyVGcj+5DIpIhIC1ML6PFVm3aqMCxEZgvXl\n2d8YU3ByejnvqScSV4VxGWPS3Z5Owjonc3LdAaesu8gDMVUqLjdjgDvdJ1Th9qpIeXF7ZFv586Gb\nMgc1N9YZjoVYx8fBGtTcU78Q3AdJr+h1f3ds0JXsTh4Xvxwo8wx9VcQlItEnD32ISCzQB9js9PZy\nvXdfYx2//OKUeZ7cXmV+Xk4T71XAAtf2mQGMEatXTgugNfDLOcRyRnGJSDfgPeAyY8wRt+llvqc2\nxtXA7ellwBbX49nAUFd80cBQfvvLtkrjcsWWgHVyc7nbtKrcXhWZAfzZ1fumN3DctSPjmW1VFWeY\nq/oG/AHrWFUBcBiY7ZreEPjBbbmLge1Y38iPu01vifWPmAx8DoR7KK4YYD6wA5gH1HFNTwQmuS3X\nHOubOuiU9RcAG7AS1idAlF1xARe42l7nur/ZG7YXcB1QBKx1u3Wtiu1V1ucF61DQZa7H1Vx/f7Jr\ne7R0W/dx13rbgBEe/rxXFNc81//Bye0zo6L31Ka4XgA2udpfCCS4rfsX13ZMBm6yMy7X86eBF09Z\nr8q2F9ZO3UHXZzkF61zKOGCca74Ab7ti3oBbb0JPbCstgaCUUn7Onw/dKKWUQhO9Ukr5PU30Sinl\n5zTRK6WUn9NEr5RSfk4TvVJK+TlN9Eop5ef+H/0VOBO00dH5AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}